Add a checkbox for the terms agreement and hooks into wp_authenticate to allow authentication or to display an error message.

wordpress-functions.php

/**
 * Add the terms agreement field
 */
function sardbaba_add_login_field() {
  ?>
    <p class="forgetmenot">
      <label for="terms-agreement">
        <input name="terms-agreement" type="checkbox" id="terms-agreement" value="agree"> <?php _e( 'I Agree to the terms and conditions' ) ?>
      </label>
    </p>
    <br>
  <?php
}
add_action( 'login_form', 'sardbaba_add_login_field' );

/**
 * This hooks into wp_authenticate (wp-includes/pluggable.php)
 */
function sardbaba_authenticate( $user, $username, $password ) {
  // Get the user object to check authentication
  $user = get_user_by( 'login', $username );

  if ( ! $user ) {
    // Return null so wp_authenticate can do standard authentication checks
    return null;
  }

  if ( empty( $_POST['terms-agreement'] ) || $_POST['terms-agreement'] != "agree" ) {
    // If user is correct but she has not agreed, replace the user object with an error
    $user = new WP_Error( 'denied', __( "<strong>ERROR</strong>: You must agree to the terms and conditions." ) );

    // User has not agreed, don't authenticate!
    remove_action( 'authenticate', 'wp_authenticate_username_password', 20 );
  }

  // Returns the user object or the error if not agreed
  return $user;
}
add_filter( 'authenticate', 'sardbaba_authenticate', 10, 3 );